Exponential Functions Lab     Name: _____________________ 

Purpose:  In this lab, you will explore exponential functions and analyze their graphs.   

Definition:  An exponential function has the form y = ab ^x , where a is any coefficient other than zero, and b is any positive number other than one.  Notice that the input value of the function, x, is in the exponent. 

Directions:  Graph the following functions on the graph paper provided.  Make sure you use the same scale for each graph!   

1.)  y = 2 ^x   2.)  y = (1/5) ^x   3.)  y = 10 ^x  

4.)  y = (6)(2 ^x)  5.)  y = (3)((1/5) ^x)   6.)  y = (2)(10 ^x) 

7.)  y = (-1)(2 ^x)  8.)  y = (-5)((1/5) ^x)   9.)  y = (1/6) (10 ^x) 
 

Questions:  Answer in COMPLETE sentences.  You may either type your responses or hand-write them on a separate sheet of paper. 

1.)  How is the graph of y = 2 ^x different from the graph of y = x²? 

2.)  What is the domain of an exponential function? 

3.)  What is the range of an exponential function when a is positive? 

4.)  What is the range of an exponential function when a is negative? 

5.)  Why can a not be zero? 

6.)  Why can b not be one? 

7.)  Why can b not be negative? 

8.)  What happens to the graph of y = 2 ^x when you put in smaller and smaller numbers for x? 

9.)  What happens to the graph of y = (1/5) ^x when you put in larger and larger numbers for x?